# RoundingMode

public final enum RoundingMode extends Enum<RoundingMode>

Specifies a rounding behavior for numerical operations capable of discarding precision. Each rounding mode indicates how the least significant returned digit of a rounded result is to be calculated. If fewer digits are returned than the digits needed to represent the exact numerical result, the discarded digits will be referred to as the discarded fraction regardless the digits' contribution to the value of the number. In other words, considered as a numerical value, the discarded fraction could have an absolute value greater than one.

Each rounding mode description includes a table listing how different two-digit decimal values would round to a one digit decimal value under the rounding mode in question. The result column in the tables could be gotten by creating a BigDecimal number with the specified value, forming a MathContext object with the proper settings (precision set to 1, and the roundingMode set to the rounding mode in question), and calling round on this number with the proper MathContext. A summary table showing the results of these rounding operations for all rounding modes appears below.

Summary of Rounding Operations Under Different Rounding Modes
Result of rounding input to one digit with the given rounding mode
Input Number UP DOWN CEILING FLOOR HALF_UP HALF_DOWN HALF_EVEN UNNECESSARY
5.5 6 5 6 5 6 5 6 throw ArithmeticException
2.5 3 2 3 2 3 2 2 throw ArithmeticException
1.6 2 1 2 1 2 2 2 throw ArithmeticException
1.1 2 1 2 1 1 1 1 throw ArithmeticException
1.0 1 1 1 1 1 1 1 1
-1.0 -1 -1 -1 -1 -1 -1 -1 -1
-1.1 -2 -1 -1 -2 -1 -1 -1 throw ArithmeticException
-1.6 -2 -1 -1 -2 -2 -2 -2 throw ArithmeticException
-2.5 -3 -2 -2 -3 -3 -2 -2 throw ArithmeticException
-5.5 -6 -5 -5 -6 -6 -5 -6 throw ArithmeticException

This enum is intended to replace the integer-based enumeration of rounding mode constants in BigDecimal (ROUND_UP, ROUND_DOWN, etc. ).

## Enum Values

#### public static final RoundingMode CEILING

Rounding mode to round towards positive infinity. If the result is positive, behaves as for RoundingMode.UP; if negative, behaves as for RoundingMode.DOWN. Note that this rounding mode never decreases the calculated value.

Example:

Rounding mode CEILING Examples
Input Number Input rounded to one digit
with CEILING rounding
5.5 6
2.5 3
1.6 2
1.1 2
1.0 1
-1.0 -1
-1.1 -1
-1.6 -1
-2.5 -2
-5.5 -5

#### public static final RoundingMode DOWN

Rounding mode to round towards zero. Never increments the digit prior to a discarded fraction (i.e., truncates). Note that this rounding mode never increases the magnitude of the calculated value.

Example:

Rounding mode DOWN Examples
Input Number Input rounded to one digit
with DOWN rounding
5.5 5
2.5 2
1.6 1
1.1 1
1.0 1
-1.0 -1
-1.1 -1
-1.6 -1
-2.5 -2
-5.5 -5

#### public static final RoundingMode FLOOR

Rounding mode to round towards negative infinity. If the result is positive, behave as for RoundingMode.DOWN; if negative, behave as for RoundingMode.UP. Note that this rounding mode never increases the calculated value.

Example:

Rounding mode FLOOR Examples
Input Number Input rounded to one digit
with FLOOR rounding
5.5 5
2.5 2
1.6 1
1.1 1
1.0 1
-1.0 -1
-1.1 -2
-1.6 -2
-2.5 -3
-5.5 -6

#### public static final RoundingMode HALF_DOWN

Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round down. Behaves as for RoundingMode.UP if the discarded fraction is > 0.5; otherwise, behaves as for RoundingMode.DOWN.

Example:

Rounding mode HALF_DOWN Examples
Input Number Input rounded to one digit
with HALF_DOWN rounding
5.5 5
2.5 2
1.6 2
1.1 1
1.0 1
-1.0 -1
-1.1 -1
-1.6 -2
-2.5 -2
-5.5 -5

#### public static final RoundingMode HALF_EVEN

Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor. Behaves as for RoundingMode.HALF_UP if the digit to the left of the discarded fraction is odd; behaves as for RoundingMode.HALF_DOWN if it's even. Note that this is the rounding mode that statistically minimizes cumulative error when applied repeatedly over a sequence of calculations. It is sometimes known as "Banker's rounding," and is chiefly used in the USA. This rounding mode is analogous to the rounding policy used for float and double arithmetic in Java.

Example: